You bet they're concerned about "zombie overload". This particle niche of the horror genre has probably run its course, at least as far as movies go. "The Walking Dead" itself goes beyond the whole zombie thing which is a big reason for its lasting success. And of course they're hoping for the same with the new series. The problem is that the character so far aren't as dynamic as Rick/Shane. Now the question is will people give it enough of a chance in order to gain similar long-term success as "TWD"? I don't know.
There is going to be plenty of opportunity for these characters to develop into legit badasses. It's just going to take some time.
A good zombie outbreak show should be 80-90% about fighting off other humans, betrayal, desperation, inverting the authority structure, and that evolution from regular person to post-apocalyptic butt-kicker. And, oh yeah, there are some zombies there, too. That stuff doesn't get old if you have the right setting and can get people invested in the characters. I agree, though, that we're off to a slow start. Not as sympathetic to the teen addict as I could be. I want the daughter to get eaten sooner rather than later. I don't like the husband, and I want the wife to become somebody I can actually root for sooner rather than later.